Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x - 7$ and $ BC = 6x + 7$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x - 7} = {6x + 7}$ Solve for $x$ $ 2x = 14$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({7}) - 7$ $ BC = 6({7}) + 7$ $ AB = 56 - 7$ $ BC = 42 + 7$ $ AB = 49$ $ BC = 49$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {49} + {49}$ $ AC = 98$